ACT (Enhanced)MathematicsHard
A statistician is analyzing the relationship between two variables, x and y. She finds that the correlation coefficient (r) between x and y is -0.92. Which of the following statements best describes the relationship between x and y?
- AThere is a strong negative linear relationship.
- BThere is a weak positive linear relationship.
- CThere is no linear relationship.
- DThere is a strong positive linear relationship.
Show answer & explanationAnswer & explanation
Correct answer: A. There is a strong negative linear relationship.
A correlation coefficient (r) ranges from -1 to +1. A value of -0.92 indicates a strong negative linear relationship because it is close to -1. The negative sign indicates an inverse relationship (as x increases, y decreases), and the magnitude (0.92) indicates strength.
Why the other options are wrong
- B. A weak relationship would have an 'r' value closer to 0 (e.g., +/- 0.2).
- C. No linear relationship would have an 'r' value very close to 0.
- D. A positive 'r' value (close to +1) would indicate a strong positive linear relationship.
Correlation Coefficient (r)
The correlation coefficient (r) measures the strength and direction of a linear relationship between two quantitative variables. It ranges from -1 to +1.
- Sign indicates direction: positive (+) or negative (-).
- Absolute value indicates strength: closer to 1 is strong, closer to 0 is weak.
- Does NOT imply causation.
Memory trick: Sign for 'S'lope, 'S'ize for 'S'trength.